- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 7. Statistical Concepts and Market Returns
- Subject 7. Chebyshev's Inequality

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**CFA Practice Question**

In 2011, a portfolio with 6 stocks had the following total return rates in percentages:

27.98%, 44.94%, 54.53%, -52.68%, 10.21%, 0.50%

The average return rate for this portfolio was 4.92% and the standard deviation was 37.66%. How confident are you that the return rates will fall within -51.57% and 61.41%?

A. 56%

B. 75%

C. 85%

**Explanation:**-51.57% is 1.5 standard deviations below the mean and 61.41% is 1.5 standard deviations above the mean. Therefore, we are confident that 1 - 1/1.5

^{2}= 56% of the return rates will fall within the specified range (Chebyshev's inequality).

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**User Contributed Comments**
5

User |
Comment |
---|---|

linr0002 |
No of stdev= (61.41-4.92)/37.66=1.5, 1-1/(1.5)^2=0.56 |

labsbamb |
K= (X-(X))/std -------> 1.5 1-(1/K*K)= 56% |

shiva5555 |
I thought 68 percent of observations would be within one standard deviation? |

soukhov |
shiva5555 there is usefull comments in LOS, chek it |

hiyujie |
Shiva5555, 68% of observation within one standard deviation is for normal distributed sample. |